Question

solve
|x-8| ≤ 4
State your answer as a compound inequality A≤X≤B:
State your answer in interval notation [A,B]:

Answer 1

To solve the inequality \( |x - 8| \leq 4 \), we can start by interpreting what the absolute value means. The expression \( |x - 8| \leq 4 \) indicates that the distance between \( x \) and 8 is at most 4.

This leads us to two inequalities:

1. \( x - 8 \leq 4 \)
2. \( x - 8 \geq -4 \)

Now we solve each inequality separately:

1. From \( x - 8 \leq 4 \):
\[
x \leq 4 + 8
\]
\[
x \leq 12
\]

2. From \( x - 8 \geq -4 \):
\[
x \geq -4 + 8
\]
\[
x \geq 4
\]

Putting these two results together, we have:

\[
4 \leq x \leq 12
\]

This can be expressed as the compound inequality:

**Answer as a compound inequality:**
\( 4 \leq x \leq 12 \)

Next, we express this in interval notation:

**Answer in interval notation:**
\[ [4, 12] \]